I am unable to change the smart campaign in the Marketing Leads Smart list under the Lead Database section. How are these leads being added to the list? How do I remove them from the list but keep them in our database?

The "Marketing Suspended" list in the Database (the icon is a man with headphones on) is a system list and cannot be edited. If you look at the system smart list's "smart list", you will see the only criteria is that "Marketing Suspended" is true. Marketing Suspended means they will not receive non-operational emails. If you would like to remove someone from this list and allow them to receive non-operational emails, then run a flow: